Basics of Electric Circuits 2

Explore the capacitor as a linear element linking charge to voltage Q = C V and i = dQ/dt. Derive energy 1/2 C V^2 and power P = V I.

Analyze a capacitor with constant voltage, where the current is the voltage derivative and stays zero, making the power zero; energy follows E = 1/2 C V^2.

examines a capacitor with a changing voltage, showing voltage exponentially rising while current decays, power peaks near 0.693 s, and energy grows from 0 to 1/2 as the capacitor charges.

Explore the capacitor's voltage over time, derive current from the voltage slope, and compute power and energy to show charging and discharging between 0–1 s and 1–2 s.

Learn how inductors in series share the same current and apply the voltage divider rule to find the voltages across L1 and L2 from the source.

Examine series capacitors where the same current flows, charges are equal, and voltages split via the voltage divider rule, linking V1, V2, and V to Ceq = 1/(1/C1+1/C2).

Explore how capacitors in parallel share the same voltage, division of current via the current divider rule, and how the total capacitance equals the sum C1+C2.

Analyzes three switch scenarios at time zero, showing zero minus to zero plus transitions and how these conditions set the initial and final voltage and inductor states.

Explore how a capacitor's initial state governs its behavior: uncharged caps act as a short at t0+, while charged caps behave as voltage sources, eventually becoming open circuits.

Examine zero and nonzero initial flux in an inductor: zero flux yields open at t0+ and short at infinite time; nonzero flux yields a current source that energizes under DC.

Analyze initial and long-term behavior of a capacitor when a switch closes, noting that capacitor voltage cannot change instantly, and compute zero-time current and infinite-time voltage via Kirchhoff rules.

Explore initial conditions in a capacitor when a long closed switch opens, show that v_C(0+) = v_C(0−) and the capacitor then acts as a voltage source, guiding subsequent currents.

Determine capacitor voltage, current, and dv/dt at t=0-, t=0+, and as t->∞ in a switch-driven circuit with a 4 V source.

Analyze initial conditions of an inductor when a switch opens, determine i(0-) and i(0+), voltages across resistors, and di/dt from v = L di/dt with L = 200.

Analyze initial conditions of an inductor in a dc circuit, compute current and voltage across resistors at t=0−, 0+, and ∞, and examine inductor's short-circuit behavior and current change rate.

Examine the initial conditions and steady-state behavior of a circuit with an inductor when the switch closes, computing the inductor current and voltages across components.

Derives the voltage across the capacitor in a first-order rc circuit under dc excitation and explains the transient and steady-state responses, including natural, zero-input, zero-state, and forced responses.

Analyze the response of a first-order RL circuit under DC excitation. Derive the general voltage across any branch and inductor current using an integrating factor, highlighting steady-state and transient responses.